The Razorbacks (16-10, 5-7 Southeastern Conference) went on a 15-2 run after leading 39-38 at halftime, and Ole Miss never recovered. The Rebels (17-9, 6-6) began rushing shots and allowing Arkansas to shoot open 3-pointers.
There are now no teams in the SEC West above .500 in conference play.
Beverley started Arkansas' run with a 3-pointer, which prompted a quick timeout by Mississippi coach Andy Kennedy, 28 seconds into the second half.
The Rebels then turned the ball over, and Beverley made another 3-pointer from almost the same spot. Beverley later added a driving layup to make it 49-40, and Kennedy called time out again with 17:03 remaining.
Another 3-pointer by Beverley, again from the right wing, made it 54-40, and the freshman provided another highlight when he tossed an alley-oop pass over his shoulder to a trailing Weems for a dunk and a 60-48 lead.
Arkansas went 12-of-28 from 3-point range -- Beverley was 6-of-11.
The Razorbacks desperately needed a win after two straight losses that damaged their NCAA tournament hopes. They went to the NCAAs last season for the first time since 2001, when Nolan Richardson was coach.
Arkansas scored the game's first eight points and led 24-16 before the Rebels went on an 11-2 run. Ole Miss never led by more than two.
Arkansas athletic director Frank Broyles announced earlier in the day he will retire at the end of this year. He has been with the school -- as football coach and now athletic director -- for five decades.